I need to compute the gravitational force on the object (m1) as a vector

2. Relevant equations

F = GMm/r^2

3. The attempt at a solution

I get 1.08e14, which is incorrect. I have a feeling I am calculating a magnitude instead of a vector, I'm just not sure what I need to do differently.

Whoa, hold on. Something is not right.

The "F = GMm/r^2" equation you mentioned is only valid if the object is at the surface of the Earth or at a greater distance away from the Earth's center that that, if you wish to use the entire mass "m2 = 6e24kg (earth)."

But the way that you worked the equation, you calculated the force on an object 16 m away from the center of the Earth, and that the entire mass of the Earth is confined within a 16 m (radius) ball or smaller ball.

As a first course of action, I'm guessing that might need to take the Earth's radius into account, if the object is ouside the Earth's surface. Could you be more clear on what coordinate system you are using when you state, "r = <0,16,0> m"? I.e, where in relationship to the center of the Earth is r = <0, 0, 0> m?

Okay, I saw the diagram. Don't use the "F = GMm/r^2" equation for this problem. Theoretically, you could use it and get the same answer, but it overly complicates things.

I believe the question is simply asking you to put the F = mg in vector notation. (F = mg is an approximation that works very well when things don't deviate too far from the surface of the earth. I'm pretty sure you should use this approximation for this particular problem.)

Using the problem statement's examples/definitions of its position vector notation, take note of which directions relate to which elements within the vector notation. Then put F = mg into this notation using the same conventions.